Structuralism in the Idiom of Determination Penultimate draft of a paper forthcoming in the BJPS. Please only cite the final version. Copyright Kerry McKenzie. 1. Introduction 2. Structuralist strategies. 3. Defining priority I: dependence or determination? 4. Structuralism in the idiom of determination 4.i Determining plurality 4.ii Determining kind properties 5. A reinvigorated eliminativism Introduction Ontic structural realism (OSR) is at its core a thesis of fundamentality metaphysics: the thesis that structure, not objects, is endowed with fundamental status. 1 Claimed both as the metaphysic most befitting of modern physics and radically at odds with more mainstream views, OSR first emerged as an entreaty to eliminate objects from our scheme of fundamental metaphysics. Such elimination was urged by Steven French and James Ladyman on the grounds that nothing less could address the ‘underdetermination of metaphysics by physics’ they claimed afflicted the status of quantum particles qua their being individuals or non- individuals – an affliction which they took to reduce any putative objectual commitment to a merely ‘ersatz form of realism’.2 Few, however, seem to have joined French and Ladyman either in acknowledging that such underdetermination exists or in attributing to it such drastic consequences. But an alternative view that physics does sanction objects, albeit merely as ontologically secondary entities, represents a different and seemingly less extreme route to the same conclusion regarding the fundamentality of structure. Indeed, what we can call the 1 E.g. French 2012, p. 122: ‘as far as the ontic structural realist is concerned, [objecthood] is to be understood as derivative at best, with structure as the fundamental ontological category.’ 2 Ladyman 1998, pp. 419-20. 1 ‘priority-based’ approach to structuralism now seems widely regarded as the more plausible of the two. But since what it means to be ‘ontologically prior’ is itself a vexed philosophical question, a stance must be taken as to how we are to understand priority before its prospects can be properly evaluated. In an earlier paper, I outlined how Fine’s notion of ontological dependence might be utilized to articulate and defend the priority-based approach to structuralism.3 Since then, however, new considerations have emerged suggesting that ontological dependence is not a relation of priority after all. As a result, the arguments outlined in that paper stand in need of reassessment. In this work, I consider the prospects for priority-based structuralism when expressed in the idiom of determination, with the aim of producing a more definitive statement of the current standing of OSR. My conclusion will be that priority-based structuralism has yet to be vindicated by our best physical theories, owing to the failure of symmetry structures to determine the world’s inventory of fundamental kinds. Nevertheless, the same symmetry considerations point toward there being renewed prospects for an eliminativist structuralism – an eliminativism, moreover, of more naturalistic appeal than that associated with OSR hitherto. The strategy that will be taken throughout will be much like that adopted before. The question of the relation between objects and structures will be examined through the lens of the most fundamental empirical theory produced to date – namely, quantum field theory (QFT). As such, many of the physical considerations that fuel the arguments of the previous paper will reappear here largely unchanged. But since the motivation for the present paper stems more from developments in our conception of fundamentality than any changes in the relevant physics, as great a portion of the paper (Sections 2 and 3) will consist of the groundwork needed to understand the claims as will be concerned with their evaluation (Sections 4 and 5). The present paper will moreover be more limited in its scope, in that it will not consider the claim that ‘structure is fundamental’ in its full generality, but focus rather on the more restricted and controversial thesis that structure alone has that status. The reason I focus exclusively on what is known as ‘strong’ (or ‘radical’) OSR over its ‘moderate’ 3 McKenzie 2014. 2 counterpart is that it now strikes me that few metaphysicians of any stripe would take issue with the claim that both objects and structures have fundamental status – making it hard to square moderate structuralism with OSR’s claim to represent a departure from metaphysical orthodoxy.4 But in any case, if the conclusion that eliminativism represents the only feasible form of structuralism is indeed the correct one to draw, then a moderate interpretation is ruled out tout court and we need not discuss it further. In what follows, then, by ‘OSR’ we will mean it as understood on its radical rendering only. Before we get started, a couple of points should be noted about the limitations of the present methodology and its focus on QFT. First of all, since QFT is not a framework that incorporates gravity, no interpretation will be given here of the standing of spacetime points, despite the fact that they are routinely presented in the literature as objects amenable to structuralist treatment. However, since those discussions have typically focused on issues of identity, the morals of the discussion of particle identity at Section 4i may be expected to transfer to them. But what that lacuna in QFT also means is that, while it represents the most fundamental physical framework that has been developed to date – indeed, is arguably the ‘most powerful, beautiful and effective theoretical edifice ever constructed in the physical sciences’ – QFT is almost certainly not a framework that correctly describes the truly ontologically fundamental.5 As such, while our conclusion may be right concerning what our best current science has to tell us about the fundamental as that science presents it, what significance that conclusion has for the fundamental simpliciter must remain an open question. Now of course, in one sense we are here in exactly the same boat as anyone working in 2017 on naturalistic fundamentality metaphysics, such as those arguing about what the world’s ‘fundamental space’ is or whether reality is fundamentally holistic.6 However, given that the roots of modern structuralism lie in the question of which, if any, of our theoretical commitments can be expected to persist as science progresses, it seems more incumbent upon structuralists to defend the value of debating fundamentality questions in advance of 4 See for example Sider 2011, passim. Esfeld and Lam (2008) is the classic exposition of ‘moderate’ OSR. 5 Duncan 2012, p. iv. 6 See e.g. North 2013; Schaffer 2010. 3 our possession of a truly fundamental theory. But while I regard this as a sorely neglected methodological question, it is too involved, and perhaps also too disheartening, to engage with here. Thus for now, we revert to type by focusing on our best current science, by assuming that that science has implications for what is truly fundamental, and by beginning to think about whether or not it recommends to us the thesis of ontic structuralism. 2. Arguments for structuralism. Under investigation is a proposition concerning the ontological fundamental: that it is structure, and only structure, to which that accolade belongs. When considering this view, it is helpful to invoke the heuristic of the world stratified into more and less fundamental ‘levels’, with OSR having something to say about the very lowest level in particular. And since OSR contests received views regarding the status of metaphysical categories, it is useful to conceive of the hierarchy of levels in a way that makes no mention of such categories – such as one based on energetic or spatial scales. Given that we are taking QFT as our physical framework, and hence Minkowski spacetime our arena, in thinking about the fundamental level we are to think about the metaphysics that emerges in the limit that spatial scales get arbitrarily small – or, equivalently, in which energies grow arbitrarily large. 7 With this picture in mind, we can now introduce the strategies structuralists have used to argue for the fundamentality of structure: the priority-based and eliminative strategies. Priority-based strategies. These strategies aim to show that, while there are objects inhabiting the fundamental level, the accolade of ‘ontologically fundamental’ belongs to structure alone. Lest this seem paradoxical, consider that Humeans, for example, will be happy to agree that the fundamental laws are those describing physical goings-on among entities inhabiting the very lowest level, and that class nominalists will agree that the fundamental properties are those located at that level too. As such, they will identify fundamental laws and fundamental properties as fundamental instances of the categories of laws and properties respectively. But each also holds that that category itself is less fundamental than some other category – the distribution of fundamental properties in the first case and 7 See Castellani 2002 for a justification of this approach. 4 collections of fundamental objects in the second. Thus in saying that the objects in the fundamental level are not ontologically fundamental, priority-based structuralists are making essentially the same kind of move. Structuralists in this sense are finding priority structure within the lowest level and between the categories that can be applied there, not postulating an additional ‘underlying’